This is something that would kind of come down to preferences and what you like, need and are comfortable using.
A couple of good free forum softwares that I would recommend (Based on actual use) are myBB and phpBB. I like myBB a little more personally.
As for paid I would go either vBulletin or Xenforo, and again this one would be based on preference. Xenforo is what this site is running on, FYI. Xenforo has a better pricing structure and is growing in popularity and use, so that's a good thing. Kind of like Wordpress, the more people that use it then the more development goes into the software. There are also lots of other developers out there creating good addons and themes for it.
It kind of comes down to preference. If you have any question about any of these in particular, I would be happy to help out if I can.
Cheers, Dean.